Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize7.0ms

Local error

Found 1 expressions with local error:

17.1b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/ x (+ (* x x) 1.0))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(/ x (+ (* x x) 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1839	192
3	5001	192

prune62.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (+ (* x x) 1.0))
17.0b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log` `associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

6.0ms	(/ 1 (+ (* x x) 1.0))
16.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ 1 (+ (* x x) 1.0))
57.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	316	470
1	1443	410
2	5001	374

prune99.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (* x x) 1.0))
0.1b	(* x (sqrt (/ 1 (+ (* x x) 1.0))))
17.0b	(sqrt (/ 1 (+ (* x x) 1.0)))
17.0b	(sqrt (/ 1 (+ (* x x) 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
48×	`sqrt-prod`
42×	`times-frac`
38×	`*-un-lft-identity`
35×	`add-cube-cbrt`
18×	`associate-r`
11×	`pow1`
10×	`add-exp-log`
8×	`associate-/r/` `add-cbrt-cube`
6×	`rem-sqrt-square` `sqrt-pow1`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-flip` `sqrt-div` `associate-l` `associate-/r` `associate-/l` `inv-pow`
2×	`pow1/2` `div-exp`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

6.0ms	(/ 1 (+ (* x x) 1.0))
19.0ms	(* x (sqrt (/ 1 (+ (* x x) 1.0))))
6.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))
7.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (+ (* x x) 1.0))
122.0ms	(* x (sqrt (/ 1 (+ (* x x) 1.0))))
73.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))
75.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	405	1012
1	1605	907
2	5001	833

prune264.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
0.3b	(/ 1 (pow x 5))
0.4b	(/ 1.0 (pow x 3))
20.2b	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

59×	`times-frac`
52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`add-cube-cbrt`
24×	`unpow-prod-down`
19×	`associate-/r*`
18×	`add-exp-log`
12×	`cube-prod`
11×	`add-log-exp`
9×	`div-exp`
8×	`frac-sub` `add-cbrt-cube` `sqr-pow`
6×	`associate-/l*`
4×	`pow1` `cube-mult` `pow-to-exp` `diff-log` `unpow3` `pow-exp` `div-inv`
3×	`sub-neg` `rec-exp` `flip3--` `1-exp` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate--r+`
1×	`pow-flip` `inv-pow` `associate--r-`

Counts

4 → 158

Calls

4 calls:

56.0ms	(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
4.0ms	(/ 1 (pow x 5))
4.0ms	(/ 1.0 (pow x 3))
31.0ms	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
47.0ms	(/ 1 (pow x 5))
36.0ms	(/ 1.0 (pow x 3))
128.0ms	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

simplify84.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	529	1089
1	2934	982
2	5001	977

prune280.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch61.0ms

Steps

Iters	Range		Point
10	13.582308112339199	112933556595576.11	248836920.91487622
8	-3802813.1226859456	-118.89002763209811	-1604.9795860088566

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample214.0ms

Algorithm

intervals

Results

130.0ms

8000×

body

valid